The present invention relates to signal processing apparatuses and methods. More particularly, the present invention relates to apparatuses and methods for recovering a transient waveform response from a signal comprised of an additive superposition of responses, such superposition occurring because the duration of a single transient response is longer than one or more of the intervals between the stimuli that cause the response.
When a system is to be tested, it is common to control the input to the system and then observe the output of the system. In such a case, the input can be called a xe2x80x9cstimulusxe2x80x9d, and the output called a xe2x80x9cresponsexe2x80x9d. It is also common for a response to be sensed and transduced into an electrical signal that can be readily measured and/or converted into numbers (digitized) for subsequent analysis. It is also common for the stimulus timing to be controlled by a digitized number stream that is transduced or converted into a form appropriate to activate the system under test. It is also common to cyclically repeat the stimulus, either to average responses together, or to test whether the system-response is affected by the repetition-rate of the stimulation.
A problem arises when the test system-response is longer than the interval between stimuli. In such cases the measured electrical signal may be an algebraic summation of the individual responses, superposed in time. Such superposition may obscure features of the individual response that are of interest. Furthermore, if the superposition occurs when the pattern of stimulation is precisely periodic, i.e., when the interval from the start of a stimulus to the start of the next stimulus is always the same, then it is not mathematically possible to compute the individual response from the superposed signal. This is true because multiple solutions will be computed, with no possibility to determine which solution is correct, since the simultaneous equations that describe the waveform have more unknown variables than simultaneous equations.
As a result, it is necessary to test the system by a series of stimuli in which the SI (Stimulus Interval, start-to-start) in the series is not uniform, i.e., by a series of stimuli in which the stimulus repetition-rate xe2x80x9cjittersxe2x80x9d.
One method for recovering the individual response from a superposed signal that uses a non-uniform stimulation sequence is called MLS (Maximum-Length Sequence). The MLS method is described in Thornton U.S. Pat. No. 5,546,956. An MLS is a pseudo-random sequence that has specific mathematical properties that permit easy calculation of a so-called xe2x80x9crecovery functionxe2x80x9d that is cross-correlated to the superposed signal to recover the individual response.
To further discuss MLS and the invention, an SI-ratio is defined by: SI ratio=(SImaxxe2x88x92SImin)/(SImin). The SI-ratio with MLS is always equal to, or greater than, unity. In some cases the MLS SI-ratio is more than 4. A major problem arises in the use of MLS if the system has responses that are affected by these SI differences Thus, MLS works if the system-response is SI-invariant, but fails if th system-response is SI-variant. Furthermore, it may not be possible to know if an error is present: if the tested system has a poor initial signal-to-noise ratio, then an SI-variant response may not be detected, yet can contribute to making the average of the response an inaccurate estimate of the system-response. Thus, there is a need for apparatuses and methods that can be used to estimate the individual system-response from an algebraic summation of superposed individual responses of a system under test, when such individual system response is SI-variant. The present invention fills this need.
Another problem arises if the system response is affected by the stimulus repetition-rate, i.e., is rate-variant. The invention uses a small SI-ratio. A small SI-ratio permits the apparatuses and methods of the invention to provide a point estimate of the system""s response at a given repetition-rate to be obtained for comparison with the response at different repetition-rates. The invention can do this, even if the system is SI-variant, because the invention can use such a small variation in SI that the size of the waveform difference is made sufficiently small so as to be not significant to the user.
A specific application of the invention relates to analysis of sensory-evoked responses at repetition-rates that are above that of stimulus-fusion. Present methods do not permit accurate analysis because the evoked-responses are longer than the time between stimuli when the repetition-rate is high enough to cause perceptual fusion of the stimuli. Clearly, for this use, apparatuses and methods are needed that can accurately recover the evoked-response, for purposes of scientific investigation, clinical testing, or screening, including children and newborns. The present invention is generally applicable to so-called xe2x80x9cSteady-Statexe2x80x9d responses that occur in several sensory-systems (Regan D, Human Brain Electrophysiology, (1989), Elsevier, N.Y., at pp. 34-42, 70-126, and 294-295), especially the auditory xe2x80x9c40-Hz responsexe2x80x9d (Regan D, op. cit. at pp. 271-275).
The present invention provides apparatuses and methods for estimating the system-response WAVEFORM to each individual stimulus in a sequence of stimuli, from a system output composed of an algebraic summation of superposed individual responses of a system under test. The invention is especially useful when the individual system-response is SI-variant or mean-rate variant, or both. The invention teaches use of selected stimulation-sequences called q-sequences or quasi-q-sequences. Both q-sequences and quasi-q-sequences have a small variation in stimulus intervals, are pseudo-periodic, have a definitive time pattern, and conform to a rule-set with both time-domain and frequency-domain constraints. The frequency-domain constraints include the Fourier coefficient vector magnitude, referred to in the invention as xe2x80x9cQ-magnitudesxe2x80x9d.
One of the time-domain constraints of q-sequences is a stimulus-interval ratio less than unity but greater than zero. One of the frequency-domain constraints of q-sequences is Q-magnitudes in the bandpass of interest of 0.5 or greater. One of the frequency-domain constraints of quasi-q-sequences is Q-magnitudes in the bandpass of interest less than 0.5 and greater than 0.01. Q-magnitudes can have values between zero and a number equal to the number of stimuli in the sequence.
The q-sequences and quasi-q-sequences are utilized for timing of stimuli in data-acquisition equipment that includes capabilities for stimulating the system under test, and for simultaneously recording the system output. The data-acquisition equipment can include additional components, such as: synchronizing means, averaging means, filtering means, amplifying means, data-rejection means, data-acquisition stopping means, simultaneous multiple q-sequence data-acquisition means, simultaneous multiple q-sequence data-acquisition means including at least one uniform stimulation-sequence means, Q-magnitude adjustment means, deconvolution set magnitude adjustment means, deconvolution set frequency adjustment means, data-analysis means, computational means, intermediate-data computational means, intermediate-data analysis means, display means, and outputting means.
The invention teaches data-analysis that utilizes deconvolution, which can be computed by any of a variety of methods. The use of deconvolution and q-sequences is indicated by the acronym for the methods of the invention: QSD (q-sequence deconvolution). The deconvolution is carried out on the recorded system output utilizing, in one form of the invention, a recovery sequence adapted from the reciprocal of the set of Q-magnitudes within the bandpass of interest combined with Q-magnitudes at the limit of the computer""s floating point numbers in bandreject regions. In one form of the invention, the frequency-domain components making up the recovery sequence can be selected, modified, or adjusted to improve recovery of the system-response.
If averaging is included in the data analysis, the deconvolution can occur before or after averaging. The data-analysis equipment can include additional components, such as: synchronizing means, alignment means, input means, averaging means, filtering means, amplifying means, noise-estimation means, data-rejection means, sweep-rejection means, simultaneous multiple stimulation-sequence data-analysis means, simultaneous multiple stimulation-sequence data-analysis means including at least one uniform stimulation-sequence means, decimation by frequency means, decimation by time means, Q-magnitude adjustment means, deconvolution-set magnitude-adjustment means, deconvolution-set frequency-adjustment means, computational means, intermediate-data computational means, intermediate-data analysis means, waveform-analysis means for analyzing said estimated system-response waveform, display means, outputting means, deconvolution by time-domain convolution of the system output by a convolution recovery sequence means, deconvolution by time-domain cross-correlation of the system output by a cross-correlation recovery-sequence means, deconvolution by division in the frequency-domain of the system output by a deconvolution set of Fourier coefficients means, deconvolution by multiplication of said system output by an inversion of a circulant matrix derived from a convolution recovery sequence means, filtering in the time-domain means, filtering in the frequency-domain means, deconvolution of single sweeps, deconvolution of combinations of one or more single sweeps, deconvolution of subaverages, deconvolution of system output without use of alignment-signal means.
The data-acquisition and the data-analysis of the present invention can be practiced using a digital computer as a component of the invention. Other equipment variations are possible. For example, the stimuli can be timed and shaped from some device such as a compact-disk player, a digital-video-disk player, an MP3 player, a video-tape player, an audio-tape player, a digital-memory player, or the like, each containing a previously-recorded storage medium or the like. Stimuli could also be delivered from a remote location using various communication means, such as cable transmission means, or radio frequency means, or satellite means.
For some practical applications, it may be desirable to separate the invention""s functions either physically or functionally. For example, the data-acquisition functions could be performed in one set of equipment, on-line, and then the data-analysis performed in other equipment, off-line. In this case the data-analysis equipment could be separated from the data-acquisition equipment by many miles, and even by time. There might be internet or stored-media communication between two such separated sets of equipment.
The invention has important applications to sensory evoked-responses at stimulus repetition-rates higher than perceived stimulus fusion because some evoked-response waveforms superpose at these repetition-rates. One such waveform is shown in FIG. 2, which is discussed in Example One found at the end of the Description section of this specification. Sensory evoked-responses have wide utility for clinical testing and disease screening, including testing newborns.
The estimated system-response waveform produced by the invention may not be the ultimate goal of the user. In such a case there may be additional processing of the information in the waveform. For example, if the invention is used in screening tests, an automatic evaluation of the estimated system-response waveform may yield a xe2x80x9cpass/no-passxe2x80x9d output only.
While the disclosed invention must be used to obtain an accurate estimate of the system-response waveform when testing a system in which the individual system-response is SI-variant and/or mean-rate variant, the invention is not limited to such systems. The invention""s waveform-estimate recovery method is fully applicable to systems in which the system-response waveform is SI-invariant and/or mean-rate invariant. For example, the present invention can be used in most applications where MLS is utilized to recover the system-response waveform since the successful use of MLS for system-response recovery implies that the response is SI-invariant and mean-rate invariant.